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1. The average salary for a certain profession is $97,000. Assume that the standard deviation of such salaries is $33,500. Consider a random sample of 54 people in this profession and let x represent the mean salary for the sample. 2. Almost all companies utilize some type of year-end performance review for their employees. Human Resources (HR) at a university’s Health Science Center provides guidelines for supervisors rating their subordinates. For example, raters are advised to examine their ratings for a tendency to be either too lenient or too harsh. According to HR, “if you have this tendency, consider using a normal distribution-----10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable “Suppose you are rating an employee’s performance on a scale of 1 (lowest) to 100 (highest). Also, assume the ratings follow a normal distribution with a mean of 50 and a standard deviation of 16. Complete parts a and b. 3. Suppose a geyser has a mean time between eruptions of 60 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 23 minutes, answer the following questions. 4. Assume the random variable X is normally distributed with mean µ = 50 and standard deviation. Complete the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(34 < X < 62) 5. The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.3 miles per gallon.

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